Fixed-Point Actions in 1-Loop Perturbation Theory

Abstract

It has been pointed out in recent papers that the example considered earlier in the O(N) sigma-model to test whether fixed-point actions are 1-loop perfect actually checked classical perfection only. To clarify the issue we constructed the renormalized trajectory explicitly in 1-loop perturbation theory. We found that the fixed-point action is not exactly 1-loop perfect. The cut-off effects are, however, strongly reduced also on the 1-loop level relative to those of the standard and tree level improved Symanzik actions. Some points on off- and on-shell improvement, Symanzik's program and fixed-point actions are also discussed.

18 pages, Latex2e

Cited by in corpus (11)

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• Fixed point action for the massless lattice Schwinger model
• Perfect Actions with Chemical Potential
• Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model
• Perfect Lattice Perturbation Theory: A Study of the Anharmonic Oscillator
• Fixed point actions and on-shell tree-level Symanzik improvement
• Lattice simulation of $(2+1)D$ phonetic solitons and the Renormalization group
• Testing the efficiency of different improvement programs
• Renormalization of $(2+1)D$ scalar Weyl spinors interactions on lattices using the Clifford groups
• Improved actions for the two-dimensional sigma-model
• Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model